Adrian had killed two people in a mudslide before making landfall, but it was quickly downgraded to a tropical storm after hitting El Salvador's Pacific coast early on Friday, where 20,000 evacuees took refuge in emergency shelters.
Television pictures showed fallen trees and torn-off branches through sheets of heavy rain as Adrian moved inland over El Salvador and toward neighbouring Honduras and Guatemala.
"The biggest threat from Adrian continues to be torrential rainfall which will likely produce flash flooding and potentially devastating mudslides over the mountainous terrain of Central America," the National Hurricane Centre in Miami said.
The storm's winds dropped to 105kph with higher gusts, although it was expected to dump up to 50cm of rain in mountain areas.
Adrian has awakened memories of Hurricane Mitch, which killed about 10,000 people, mainly in Honduras and Nicaragua, with mudslides and flooding in 1998.
Streets in La Libertad were deserted as people sought refuge in their homes after power went out, rains sprayed across increasingly agitated surf and waves pounded at the pier.
"The electricity has gone out, the wind is getting stronger and it's raining non-stop," said Jorge Alberto Turcios, a guard at a restaurant in La Libertad.
"The waves are getting higher; there's not a soul on the street"
Jorge Alberto Turcios
"The waves are getting higher; there's not a soul on the street," Turcios said in a telephone interview.
Earlier, Saca broadcast an appeal for his citizens to obey evacuation requests.
"We understand that they are guarding their belongings, but lives are worth more than anything," he told Radio La Chevere.
Authorities evacuated about 14,000 people from low-lying coastal areas, in some cases using helicopters as waters rose. Most were taken to improvised shelters at schools, where classes were cancelled.
Rivers rose in El Salvador and in neighbouring Honduras, both nations devastated by Hurricane Mitch - a Caribbean storm - in 1998.
The rains began to wash out some roads in both countries, officials reported.
Already one death was indirectly linked to the storm - a military pilot died on Wednesday when he crashed a small plane that he was ferrying from San Salvador's civilian airport to a military base as a precaution against the heavy winds.
Officials did not give the cause of the crash.
State of emergency
Honduras declared a state of emergency as Adrian approached.
People were evacuated from
low-lying coastal areas
"We are preparing for the worst," President Ricardo Maduro said late on Thursday and his government sent aid supplies to vulnerable areas near the border with El Salvador.
Across the region, families stocked up on food and supplies.
"We are all worried. People are scared because we all lost something with Mitch," said housewife Maria Esperanza in Guatemala's Puerto San Jose late on Thursday.
Two men were killed and two injured in Guatemala on Thursday when a mudslide blamed on Adrian swallowed them as they dug a ditch near the Mexican border.
But Guatemalan President Oscar Berger played down comparisons with 1998: "This will not be like Mitch, we think we will have rains in coastal areas and some damage, but we are in a state of alert and ready to attend to the population."
The US State Department issued a warning to travellers in El Salvador, Guatemala, Honduras, Belize and Nicaragua.
The National Hurricane Centre has predicted that 11 to 15 tropical storms will form this season in the eastern Pacific.
Six to eight are expected to become hurricanes, which are ranked in ascending categories of strength from 1 to 5.